# Complex or imaginary shapes?

Algebra Level 5

The absolute value of a complex number would be the distance between the complex number to the origin $$(0,0)$$ in the complex plane. Or in other words, $|a+bi| =\sqrt { { a }^{ 2 }+{ b }^{ 2 } }$ So for $$|z|=n$$, the possible values of $$z$$ would form a circle of radius $$n$$ centered at the origin on the complex plane.

Now, supposing I create a new function: $$\ddagger a+bi\ddagger =|a|+|b|$$

And all of the possible values of $$z$$ in $$\ddagger z\ddagger =2015$$ forms a shape of area $$A$$ on the complex plane.

Find $$\left\lfloor A \right\rfloor$$

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